We investigate the emergence of charge waves and their temporal dynamics in one-dimensional Su-Schrieffer-Heeger (SSH) topological chains. Contrary to the conventional view that charge oscillations are suppressed in gapped topological systems with preserved chiral symmetry, we show that such oscillations can indeed occur. The general condition for an arbitrary oscillation period is analyzed, and we find that the charge waves propagating along the chain do not depend on its topology, except at the edges, where both topological phases exhibit essential differences. In chains with inequivalent atoms within the SSH unit cell, we observe regular long-period sublattice oscillations that appear simultaneously with even-odd charge oscillations. Furthermore, we study the nonequilibrium time dynamics in SSH chains. After a quench, the time evolution of the local density of states and charge occupancies exhibit clear dynamical fingerprints of the underlying topological phases. Our results demonstrate that transient charge dynamics can distinguish topologically trivial and nontrivial phases in real time by detecting the presence of topologically protected edge states.

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• Charge density waves
• Charge dynamics
• 1-dimensional systems
• Quantum wires
• Topological insulators
• Second quantization
• Tight-binding model